BP's incoming chief executive, Bob Dudley, has reassured the City that the company will probably end up paying out less than the committed $20bn in compensation for those affected by the Gulf oil spill.

The White House ordered the company to pay $20bn into a compensation fund over three and a half years, making it clear that further payments may be required.

Although BP still does not know how much it will have to contribute, Dudley's comments that the $20bn already pledged should cover these claims reflect BP's growing confidence that it can emerge from April's Deepwater Horizon disaster in a relatively strong position.

It is understood the company also informed City analysts at a meeting in London on Friday that a facility allowing any unpaid amounts from the fund to be paid back to BP has now been set up.

Analysts even believe BP will soon be able to resume paying dividends, with Citigroup predicting it could do so as early as February, when it reports its full-year results.

Dudley, who formally takes over from Tony Hayward on 1 October, stressed that the decision to suspend the dividend in June was for liquidity reasons, to conserve cash to pay for the spill costs.

Since then, BP has raised about $10bn from asset sales and its costs from the clean-up operation are tailing off because oil has stopped flowing from the stricken well. Because the size of the spill has stopped growing and has been measured, the extent of BP's potential liabilities have also become clearer.

Dudley also told analysts the estimate BP made in July of $32.2bn for its total liabilities from the spill – officially the biggest in US history – remained reasonable. This assumes BP is not found to have been grossly negligent, in which case its liabilities would soar.

BP has privately been confident for some time that the compensation fund – now being run by White House appointee Ken Feinberg – would not pay out anywhere near $20bn. About $500m in claims have been paid out in just under five months and the claims process will remain open for three years. It is thought Dudley has been in regular contact with Feinberg.

But Dudley did acknowledge the ongoing risks in the aftermath of the disaster when he said one of BP's priorities was to retain its licence to operate in the US. BP makes more than a third of its total revenue from producing oil and gas from its operations in the Gulf of Mexico and onshore in the US, and some politicians have called for the company to be banned from operating there. One analyst at the meeting told the Guardian: "He was upbeat. I wouldn't say he was optimistic but he was definitely confident about BP's position and seemed more comfortable."

This week retired coastguard Admiral Thad Allen, who is handling the BP oil spill crisis on behalf of the US government, is expected to explain in more detail how the level of pollution in the Gulf will be measured, which will go a long way to determining the amount of reparations BP must pay. BP has hired scientists as subcontractors to work alongside federal agencies and universities to take samples, which has led some to question whether the company could seek to influence the results. A spokesman said there was nothing untoward about assisting the effort.

Jackie Savitz, a marine biologist from campaign group Oceana, said some scientists were concerned about BP being able to influence the process, although no evidence has emerged that this has taken place.

"There is no question that BP would be less committed than the government to showing the full impact and degradation caused to the environment since the company will be on the hook for the damages. The question is whether the government will allow BP to influence its analysis.

"The scientists I have spoken to are aware of the possibility that BP could try to influence the process, and that there can be other pitfalls from the company participating. For example, with BP constantly looking over their shoulders when they collect data, they have to do it 100% right otherwise BP could challenge it in court later."